House Area B01Da1

1. **Stating the problem:** We have a symmetric house-like shape composed of a peaked roof, a rectangular body, and semicircular bulges on both sides. The given numbers likely represent dimensions or lengths related to the shape. 2. **Understanding the shape and given values:** - The rectangular body has dimensions possibly related to $97$ (width) and $38$ (height). - The semicircular bulges on each side have radii possibly related to $29$. - The peaked roof height or other lengths might be related to $33$, $32$, and $29$. 3. **Goal:** Calculate the total area of the shape using simple grade 8 level calculations. 4. **Formulae and rules:** - Area of rectangle: $$A_{rect} = width \times height$$ - Area of semicircle: $$A_{semi} = \frac{1}{2} \pi r^2$$ - Area of triangle (roof): $$A_{tri} = \frac{1}{2} \times base \times height$$ 5. **Calculations:** - Rectangle area: $$A_{rect} = 97 \times 38 = 3686$$ - Semicircle area (two semicircles make a full circle): $$r = 29$$ $$A_{circle} = \pi \times 29^2 = \pi \times 841 \approx 3.1416 \times 841 = 2642.08$$ $$A_{semi\_total} = A_{circle} = 2642.08$$ - Roof area (assuming peaked roof is a triangle with base $97$ and height $33$): $$A_{tri} = \frac{1}{2} \times 97 \times 33 = 0.5 \times 3201 = 1600.5$$ 6. **Total area:** $$A_{total} = A_{rect} + A_{semi\_total} + A_{tri} = 3686 + 2642.08 + 1600.5 = 7928.58$$ 7. **Final answer:** The total area of the house-like shape is approximately $$7928.58$$ square units.